Behavior and Properties of Functions

This video tutorial covers sinusoidal graphs, focusing on functions that can be modeled by sine or cosine functions. It includes detailed analysis of functions f(x), G(θ), H(θ), and K(θ), explaining how to find their period, frequency, amplitude, and midline. The video also explores the behavior of these functions over different intervals, discussing concepts like concavity and rate of change. The tutorial is part of the AP pre-calculus curriculum, specifically topics 3.4 and 3.5.

What type of functions can model sinusoidal graphs?

• Linear and quadratic

• Sine and cosine

• Exponential and logarithmic

• Polynomial and rational

What is the period of the sinusoidal function f(x) if measured from peak to peak?

• 4

• 2

• 3

• 5

How is the frequency of a sinusoidal function determined?

• By adding the period

• By taking the reciprocal of the period

• By halving the period

• By doubling the period

What is the midline of the function f(x) if the highest value is 3 and the lowest value is -1?

• y = 0

• y = 1

• y = 3

• y = 2

What is the amplitude of the function f(x) if the midline is y = 1 and the highest value is 3?

• 1

• 2

• 3

• 4

What is the period of the sinusoidal function G(θ) if it stretches from 0 to π/2?

• π/2

• π/4

• π

• 2π

What is the frequency of the function G(θ) if the period is π/2?

• π

• 2/π

• 1/π

• π/2

What is the midline of the function G(θ) if the highest value is 4 and the lowest value is -2?

• y = 2

• y = 1

• y = 3

• y = 0

What is the amplitude of the function G(θ) if the midline is y = 1 and the highest value is 4?

• 3

• 2

• 1

• 4

What is the period of the sinusoidal function H(θ) if it stretches from 0 to π?

• 3π

• 2π

• π

• π/2